Problem: Solve for $x$ and $y$ using substitution. ${-5x-y = -7}$ ${y = -4x+6}$
Explanation: Since $y$ has already been solved for, substitute $-4x+6$ for $y$ in the first equation. ${-5x - }{(-4x+6)}{= -7}$ Simplify and solve for $x$ $-5x+4x - 6 = -7$ $-x-6 = -7$ $-x-6{+6} = -7{+6}$ $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -4x+6}\thinspace$ to find $y$ ${y = -4}{(1)}{ + 6}$ $y = -4 + 6$ $y = 2$ You can also plug ${x = 1}$ into $\thinspace {-5x-y = -7}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ - y = -7}$ ${y = 2}$